The latest graduate of the Tuna Tree is 35-year-old Eric Mangini, who this year became head coach of the Jets. Mangini, who like Belichick graduated from Wesleyan in Connecticut, began as an intern for Belichick in Cleveland in 1995; worked for Parcells on the Jets from 1997-99, then went with Belichick to New England. He is more a product of Belichick than Parcells, having finally worked his way up to defensive coordinator for the Patriots last year when Crennel left for Cleveland.

For a long time, the perception was that Parcells and Belichick were joined at the hip. Belichick first achieved prominence as the 34-year-old defensive coordinator of the 1986 Giants, one of the great teams of the ’80s. He went on to Cleveland after the Super Bowl victory following the 1990 season, but was just 37-45 there before being fired when the team moved to Baltimore after the 1995 season.

Then Belichick rejoined Parcells in New England and later went with him to the Jets with the assurance that he would be the Tuna’s heir. He was — for a day — before deciding he didn’t want the job and moving on to the Patriots.

Neither man has talked about it, but the general perception is that Belichick wanted to get out from under the Tuna’s shadow — Parcells remained as the Jets’ director of football operations. Belichick wasn’t free to join the Patriots until a settlement was reached with the Jets that included a first-round draft choice as compensation.

Many people considered his hiring a strange choice by the Patriots, given Belichick’s flop in Cleveland.

“I just thought he was one of the smartest people I’d ever met,” Patriots owner Robert Kraft says of Belichick, who he hired despite calls from respected football people telling him it was a bad choice.

It wasn’t. Belichick’s three Super Bowls in four years earned him the “genius” label easily given but rarely lived up to, except perhaps by Walsh.

Belichick’s proteges think he’s in that category.

“I wouldn’t mind being considered a genius,” said Crennel, who actually is five years older than Belichick. “I might not be there yet, but I can work towards that.”

At this point, the tree is as much Belichick’s as Parcells — just as Holmgren spawned most of the Walsh-bred coaches.

Weis, a glorified gofer on the 1990 Giants, became a star offensive coordinator as the Patriots won their Super Bowls. Crennel, defensive line coach on the Giants in the ’80s, became the same on defense — even as a coordinator under a defensive coach.

But it varies.

Coughlin never worked for Belichick and still is very close to Parcells, who has called him “the best coach I ever was associated with.” In 2003, after being fired by Jacksonville and before being hired by the Giants, Coughlin spent part of his summer in the Dallas training camp, exchanging ideas with his old boss.They remain close, but as division rivals they don’t help each other out any more.

In hindsight, it’s easy to suggest that Belichick was the key to Parcells’ success with the Giants.

Look at tapes of the 2002 Super Bowl, when the Patriots, 14-point underdogs, upset an explosive St. Louis team.

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New England’s defense in that game was eerily similar to the one the Giants used 11 years earlier against an equally skilled Buffalo team. Often no more than one or two down lineman and as many as seven defensive backs were on the field. And just as the Giants conceded the run to Thurman Thomas in that ’91 game, the Patriots dared Mike Martz to run Marshall Faulk, and he didn’t — until it was too late.

In the end, call it a very productive collaboration between two extremely talented football men.

They’ll never be pals: Belichick will never go deep-sea fishing with Parcells or accompany him to Saratoga — two of the Tuna’s passions. And Parcells will probably never go with Belichick to a Bon Jovi concert.

But their new relationship is build on common football interests.

“He knows what my problems are. He’s someone to talk to about what are you going to do here and what are you thinking about there,” Parcells says.

And, perhaps, to talk about a new batch of up-and-coming coaches.